Just how rare are these brown pandas in Minecraft, I didn't see stats on the wiki. So basically what percent chance is there that a brown panda will spawn?
Minecraft Java Edition – How Rare Are Brown Pandas?
minecraft-java-edition
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When a chunk is populated, the dungeon generation is always tried 8 times independently at random positions in the chunk. For each generation, given a random size (5x5, 5x7, or 7x7, excluding walls), a dungeon is generated only if the ceiling and floor blocks are solid and there are 1~5 air blocks in the lower half of the surrounding walls.
Possibility? That's complicated to calculate because the probability distribution of air blocks is more complicated and that depends on this. However, you can certainly qualitatively assert that double dungeon is rare. I assert the existence of triple dungeon.
Mobs cannot spawn in a well lit area, but only a single square is enough to allow spawning. The light level must be 8 or higher to prevent spawning, meaning no cube can be more than 7 steps from a torch. You have to count vertical steps too, so a torch two squares off the floor can only be five horizontal steps from any floor square.
In addition, spiders can climb up walls, and thus are harder to keep out than other mobs. But the fact that you have creepers and zombies as well indicates that you have a lighting issue. Creeps can also fall down from heights farther than they would choose to walk; if the cliff above your balcony can spawn mobs, you may wish to light it or fence it to prevent mobs from pushing each other off the edge and falling to your balcony.
After you posted the screenshots, I made this graphic, illustrating some of the squares that have insufficient light. The green dot means that area is light level 8 or higher (within 7 cubes of a torch). A red dot indicates it is light level 7 or lower, and mobs can spawn there. As you can see, there is a large splotch of darkness on the right side of your balcony, where it is widest. Add a few more torches and everything should be fine. I did miscount a bit when creating the graphic: the leftmost two red dots should be green, as they are 7 cubes from the torch that is just out of sight on the bottom left. This leaves 5 squares visible in the image that are below light level 8.
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Best Answer
The wiki states that pandas spawn with a randomized personality. Each panda has a dominant gene and a recessive gene, each of which is randomly selected from the 7 possible genes. For a panda to be brown, both genes must be the brown type. Without taking mutation into account, the probability of a given panda being spawned as brown is then 1⁄7 x 1⁄7 = 1⁄49 or 2.04%.
However, there is also the mutation mechanic to consider: every gene has a 1⁄32 chance of mutating into something else, and this applies to spawned as well as bred pandas. This complicates things a quite a bit. Because of mutation we have to consider several additional possibilities:
1. A panda with exactly one brown gene can mutate into a panda with two brown genes:
According to the wiki table of possible gene configurations, there are 12 possible gene pairs that have exactly 1 brown gene, out of the total of 49 possible pairs. In order for a panda with exactly one brown gene to become fully brown, the non-brown gene must mutate, and it must turn into a brown gene. The probability for this is calculated by the following equation: P(only the non-brown gene mutating) = P(any gene to mutate) x P(any gene to not mutate) x P(the non-brown gene to be the one that does mutate) = 1⁄32 x 31⁄32 x 1⁄2 = 31⁄2048. Then there is the 2⁄16 chance that it will become brown: 31⁄2048 x 2⁄16 = 62⁄32768. The probability of a panda spawning with exactly one brown gene and mutating into one with two brown genes is then: 12⁄49 x 62⁄32768 = 744⁄1605632 or 0.0463%.
2. A panda with no brown genes can mutate into a panda with two brown genes:
Of the 49 possible gene configurations, 36 have no brown genes at all. This kind of panda then has a natural occurrence of 36⁄49. The probability for both genes mutating is 1⁄32 x 1⁄32 = 1⁄1024. The probability of both mutated genes becoming brown is 2⁄16 x 2⁄16 = 1⁄64. The probability of both genes mutating and both becoming brown is then 1⁄1024 x 1⁄64 = 1⁄65536. The probability of a panda spawning without any brown genes then mutating into one with two brown genes is then 36⁄49 x 1⁄65536 = 36⁄3211364 or 0.00112%.
3. A brown panda can mutate into a not-brown panda:
A brown panda will become not-brown if either gene mutates. The probability of either gene mutating uses the equation P(A or B) = P(A) + P(B) - P(A and B) = 1⁄32 + 1⁄32 - (1⁄32 x 1⁄32) = 2⁄32 - 1⁄1024 = 63⁄1024.
If the mutating gene stays brown, nothing will happen. There is a 2⁄16 chance of that, so there is a 14⁄16 chance of mutating into something else: 63⁄1024 x 14⁄16 = 882⁄16384.
Since brown pandas occur as 1⁄49 and the chance of a brown panda turning into a not-brown panda is 882⁄16384, there is a 1⁄49 x 882⁄16384 = 882⁄802816 or 0.109% chance of a panda being spawned with two brown genes and mutating into one with less than two brown genes.
Taking all this into consideration, the chance of a brown panda getting spawned is as follows:
The chance of a panda being spawned with two brown genes and not mutating: 1⁄49 x (31⁄32 x 31⁄32) = 1⁄49 x 961⁄1024 = 961⁄50176 or 1.915%
Plus the chance of getting a panda with exactly one brown gene that mutates into a fully brown panda: 0.04633%
Plus the chance of getting a panda with no brown genes that mutates into a fully brown panda: 0.00112%
Minus the chance of a brown panda mutating into a not-brown panda: 0.1098%
Summing these chances: 1.915% + 0.04633% + 0.00112% - 0.1098% = 1.853% for a given naturally occurring panda to be brown.